1. Trusses

2. Planar Trusses
A Truss is a structure composed of slender members (two-force members) joined together at their end points. Joints are modeled by smooth pin connections. Members are either under tension or compression.
Joints are usually formed by bolting or welding the members to a common plate, called a gusset plate, or simply passing a large bolt through each member.

3. Basic Truss Element
When all members of a truss lie in a single plane, that truss is planar. A plane truss is rigid if it does not change shape when subjected to a general system of forces at it joints.
The truss must maintain its shape and remain a rigid body when detached from it supports.
The simplest stable or rigid form of a truss is a triangle, which is the basic truss element:

4. Rigid Truss
To prevent collapse, the form of the truss must be rigid. For example in the following figure, add member AC to stabilize the truss:

5. Simple Truss
The basic truss ABC can be extended by adding new members BD and CD to the existing joints B and C and connecting them to form a new joint D. Providing that D does not lie on a line through BC the new truss will be rigid.
Further extend the basic truss by repeating this process. A truss constructed by this procedure is called a simple truss. A B C D E

6. Type of Trusses There are two types of trusses: Roof trusses, and
Bridge trusses.
The following table shows some of the roof trusses:
Warren
English or Howe
Howe

7. Bridge Trusses
Howe
Pratt
Warren

8. Statically Determinate Truss
A simple truss is formed by taking the basic truss element and adding two members and one joint. If the number of joints is represented by j, the number of reaction forces by r, and the number of members by m, then the following formulas show which type of truss we have:
If a simple plane truss (r=3), is statically determinate, then:
m = 2 j – 3

9. Statically Determinate Truss
Unbraced truss
8 < 2 ( 6 ) - 3
Truss instability
Braced truss
9 = 2 ( 6 ) - 3

10. Examples Statically Determinate: m = 7 (members)
j = 5 (connection joints)
r = 3 (two for pin and one for roller)
m = 2j - r
Statically Indeterminate:
m = 8
j = 5
r = 3
m > 2j - r
Statically Unstable:
m = 6
m < 2j - r

11. Trusses
Part 2

12. Analysis of Trusses Truss Analysis Internal equilibrium
External equilibrium
Internal equilibrium
To find the force in each member
To find the reaction forces
Method of joints
Method of sections

13. External Equilibrium
Determine the support reactions in the joints of the following truss.